You are dealing with asymmetrickite. The axis of symmetry is the line (BD).

You add congruent figures smmetrical to the existing axis. Therefore corresponding points of the squares (You can take the vertices or the center, or midpoints of sides,...) are connected by lines perpendicular to the axis of symmetry. That means these connections are parallels. Thus the new figur is a trapezium.

If you want to proof that this trapezium is symmetric too, then show that the lines which don't intersect the axis (blue lines) are symmetric to each other.